8 IV April 2020 http://doi.org/10.22214/ijraset.2020.4129 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue IV Apr 2020- Available at www.ijraset.com
Roman Coloring of Bull Graphs and related Graphs
Preethi K Pillai1, J. Suresh Kumar2 1, 2Assistant Professor, PG and Research Department of Mathematics, N.S.S. Hindu College, Changanacherry, Kerala, India 686102
Abstract: The Bull graph is a graph with 5 vertices and 5 edges consisting of a triangle with two disjoint pendant edges. In this paper, we obtain the Roman coloring of the Bull graph and related graphs such as Middle graph, Total graph, Splitting graph, Degree splitting graph, Shadow graph and Litact graph of the Bull graph. Keywords: Graph, Roman coloring, Bull graph
I. INTRODUCTION Graph coloring take a major stage in Graph Theory since the advent of the famous four color conjecture. Several variations of graph coloring were investigated [5] and still new types of coloring are available such as −(Sigma) coloring [4] and Roman coloring [6, 7]. In this Paper, we consider the proper coloring for the Bull graph and related graphs. By a graph, we mean a finite undirected graph without loops and parallel edges. The Bull graph is a planar undirected graph with five vertices and five edges in the form of a triangle with two disjoint pendant edges. There are three variants of Bull graph, the name being derived from the fact that the structure of the graph is meant to represent the face of a “Bull”.